With the best will in the world, having 10 days to work on yourself isn't going to make that much of an impact. Body recomposition, which is what you're after (losing fat, gaining muscle) is a much longer endeavor.
My recommendation would be to try and do that same sort of workout that your PT puts you through; although you currently find it exhausting, over time you will adapt to it, provided you're recovering adequately, and then do your self-exercise as you normally do.
When looking at making changes to your body, consistency over time is the most important thing.
What I'd also look at is the other aspects of your life with regards to your goals; Are you eating enough? Are you getting enough sleep? Are you stretching and doing mobility work (which can help with back pain). These are the often neglected things that you can work on with your time off.
How's your eating? This is the key to fat loss. If your diet isn't great, or you're eating too much or not enough, take the time off to figure out how to eat better and do meal prep / cook some simple, nutritious food. Maybe take a quick cookery class, spend a day in the kitchen and learn a few recipes. There are a lot of resources online for healthy meals, try some and find some you like!
How's your recovery? If you don't feel like you're recovering from training sessions well enough, then have a look at your sleeping environment and see if you can improve it at all (again, searching for information about better sleep should yield a host of results). Go treat yourself to a massage, take a few yoga classes to work on your flexibility and chill out a bit.
If you feel completely burned out from your training, and you've been hitting it hard for a couple of months, then it doesn't hurt to take a week off and just do some light exercise instead. Go swimming, go for a hike, take a yoga class (though some of those can actually be pretty intense).
I know this isn't the answer you want... telling you to hit the gym for 17 hours a day, work every body part 121 times in those 10 days and generally wreck yourself would be a much sexier answer, but honestly, you're doing the right thing with regards to your training at the moment, just stick at it, it takes time to make changes.